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D₇×#107 #89651

order	448
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Splittings

Fitting	C₇×#107 ⋊ C₂
Sylow	C₇ ⋊ C₂×#107

Subgroups

	subgroup	G/H
center	C₂²	D₄×D₇
commutator	C₄×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₇×#107	C₂
socle	C₂²×C₇	C₂×D₄
prime radical	C₂²×D₇	D₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	#107	D₇
hypocenter	C₇	C₂×#107
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 3 generators on 19 points:

(5,6,10,12,8,11,7,9)(13,14,16,18,19,17,15);(1,2,3,4)(6,9)(7,10)(11,12);(14,15)(16,17)(18,19)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#357, #11726943, #11726953, …
maximal normal subgroup of	D₇×#357, #11726943, #11726953, …
maximal quotient of	D₇×#335, #11726323, #11726326, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 413);