C₂×C₅×D₁₃₄₃ #41001721

order	26860
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₃₄₃
unambiguous semidirect product	(C₂×C₁₇)⋊(C₅×D₇₉)
unambiguous semidirect product	(C₂×C₇₉)⋊(C₅×D₁₇)

Splittings

Fitting, socle	C₂×C₅×C₁₇×C₇₉ ⋊ C₂
derived, Hall	C₁₇×C₇₉ ⋊ C₂²×C₅
Hall	C₅×C₁₇×C₇₉ ⋊ C₂²
Hall	C₅×C₇₉ ⋊ C₂×D₁₇
Hall	C₅×C₁₇ ⋊ C₂×D₇₉
Sylow	C₇₉ ⋊ C₂×C₅×D₁₇
Sylow	C₁₇ ⋊ C₂×C₅×D₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₃₄₃
commutator, cosocle, hypocenter	C₁₇×C₇₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₇₉	C₂
LCS	G ▷ C₁₇×C₇₉
UCS	C₁ ◁ C₂×C₅

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 13430

A minimal faithful permutation representation — 2 generators on 103 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98,99,100,101);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,81,83,85,87,89,91,93,95,96,94,92,90,88,86,84,82)(102,103)

Conjugacy classes & character table

6730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26860, 31);

C2×C5×D1343 #41001721