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#28334336

order	13696
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

C₁₀₇ ⋊ #1292

Subgroups

	subgroup	G/H
center	C₂²	C₁₀₇⋊#95
commutator	C₂×C₄×C₁₀₇	C₄²
Frattini	C₂×C₄²	C₂×D₁₀₇
Fitting	C₂×C₄⋊C₈×C₁₀₇	C₂
socle	C₂²×C₁₀₇	#95
prime radical	C₂³×C₁₀₇	C₄⋊C₄
cosocle	C₂×C₄²×C₁₀₇	C₂²
hypercenter	C₂×C₄⋊C₈	D₁₀₇
hypocenter	C₁₀₇	#1292
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6848

Polycyclic presentation:

2^7,107|a^2=d,b^2=e,c^2=fg,d^2=g,e^2=fg,b^a=bc,c^a=cf,e^a=efg,h^a=h^106,d^b=dg

Conjugacy classes & character table

2152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13696, 2385);