C₅×C₇⋊D₂₈₇ #34095601

order	20090
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₅×C₇⋊D₂₈₇
unambiguous semidirect product	C₇⋊(C₅×D₂₈₇)

Splittings

Fitting, socle, Hall	C₅×C₇²×C₄₁ ⋊ C₂
derived, Hall	C₇²×C₄₁ ⋊ C₂×C₅
Hall	C₅×C₇² ⋊ D₄₁
Hall	C₅×C₄₁ ⋊ C₇⋊D₇
Sylow	C₇² ⋊ C₅×D₄₁
Sylow	C₄₁ ⋊ C₅×C₇⋊D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₅	C₇⋊D₂₈₇
commutator, cosocle, hypocenter	C₇²×C₄₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₄₁	C₂
LCS	G ▷ C₇²×C₄₁
UCS	C₁ ◁ C₅

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 10045

A minimal faithful permutation representation — 3 generators on 60 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)(43,44)(45,46)(47,48)(50,51)(52,53)(54,55)(56,57,58,59,60);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(49,50,52,54,55,53,51);(42,43,45,47,48,46,44)

Conjugacy classes & character table

5030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20090, 24);

C5×C7⋊D287 #34095601