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H(5,𝔽2)×C491 #30628240

order15712
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C24×C491 · Schur multiplier (H2) = C25

Aliases

direct productH(5,𝔽2)×C491

Subgroups

subgroupG/H
center, socleC2×C491C24
commutator, Frattini, cosocleC2C24×C491
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C491 ◁ G

166 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3928

Conjugacy classes & character table

8347 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44536893, #44536903, #44536912, …
maximal subgroup of#453×C491, #455×C491, B(4,𝔽2)×C491, …
maximal normal subgroup of#453×C491, #455×C491, B(4,𝔽2)×C491, …
maximal quotient of#518×C491, #520×C491, #534×C491, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15712, 49);