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D₇×#95 #89435

order	448
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₇×#95 ⋊ C₂
Sylow	C₇ ⋊ C₂×#95

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₇
commutator	C₂×C₇	C₂×C₄²
Fitting	C₇×#95	C₂
socle, cosocle	C₂³×C₇	C₂³
prime radical	C₂³×D₇	C₂²
hypercenter	#95	D₇
hypocenter	C₇	C₂×#95
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ #95

330 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:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#327, #11726056, D₇×#328, …
maximal normal subgroup of	D₇×#327, #11726056, D₇×#328, …
maximal quotient of	D₇×#336, #11726414, #11726415, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 197);