C₄₇×C₇⋊D₇ #17987198

order	4606
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₄₇×C₇⋊D₇
unambiguous semidirect product	C₇⋊(D₇×C₄₇)

Splittings

Fitting, socle, Hall	C₇²×C₄₇ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₇²×C₄₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₄₇

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 2303

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(49,50)(51,52)(53,54)(56,57)(58,59)(60,61);(55,56,58,60,61,59,57);(48,49,51,53,54,52,50)

Conjugacy classes & character table

1222 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#64424, C₄₇×#64425, C₄₇×ΓL(1,𝔽₈)⋊D₇, …
maximal normal subgroup of	C₄₇×#64424, C₄₇×#64425, C₄₇×ΓL(1,𝔽₈)⋊D₇, …
maximal quotient of	C₄₇×C₃⋊(C₇⋊D₇), C₃×C₄₇×C₇⋊D₇, C₅×C₄₇×C₇⋊D₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4606, 9);

C47×C7⋊D7 #17987198