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C₇×#66776 #14558668

order	2380
isoclinism	isoclinic class of #66776
automorphism	?
homology	Abelianization (H₁) = C₄×C₇ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Fitting, socle, Hall	C₅×C₇×C₁₇ ⋊ C₄
derived, Hall	C₅×C₁₇ ⋊ C₄×C₇
Hall	C₇×C₁₇ ⋊ AGL(1,𝔽₅)
Hall	C₅×C₇ ⋊ #595
Sylow	C₁₇ ⋊ C₇×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₇×#595

Subgroups

	subgroup	G/H
center, hypercenter	C₇	#66776
commutator, hypocenter	C₅×C₁₇	C₄×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₇	C₄
prime radical	C₇×D₈₅	C₂
cosocle	D₈₅	C₂×C₇
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 595

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5,6,7)(9,10,11,13)(12,15,16,20)(14,19,17,18)(21,23,24,22)(26,27,28,29);(8,9,12,17,13,18,22,24,20,15,21,23,19,10,14,16,11)(25,26,29,27,28)

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×#13133324, C₅×C₇×#66776, C₇×#13133344, …
maximal normal subgroup of	C₅×C₇×#66776, C₄₉×#66776, C₇²×#66776, …
maximal quotient of	C₇×#13133324, C₅×C₇×#66776, C₇×#13133344, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2380, 15);