C₂×C₃×D₁₀₇₉ #27188299

order	12948
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×D₁₀₇₉
unambiguous semidirect product	(C₂×C₈₃)⋊(C₃×D₁₃)

Splittings

Fitting, socle	C₂×C₃×C₁₃×C₈₃ ⋊ C₂
derived, Hall	C₁₃×C₈₃ ⋊ C₂²×C₃
Hall	C₃×C₁₃×C₈₃ ⋊ C₂²
Hall	C₃×C₈₃ ⋊ C₂×D₁₃
Sylow	C₈₃ ⋊ C₂×C₃×D₁₃
Hall	C₃×C₁₃ ⋊ C₂×D₈₃
Sylow	C₁₃ ⋊ C₂×C₃×D₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₀₇₉
commutator, cosocle, hypocenter	C₁₃×C₈₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₈₃	C₂
LCS	G ▷ C₁₃×C₈₃
UCS	C₁ ◁ C₂×C₃

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 6474

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

Conjugacy classes & character table

3246 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12948, 38);

C2×C3×D1079 #27188299