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C2×H(5,𝔽2)×C229 #28411196

order14656
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C25×C229 · Schur multiplier (H2) = C29

Aliases

direct productC2×H(5,𝔽2)×C229

Subgroups

subgroupG/H
center, socleC22×C229C24
commutator, Frattini, cosocleC2C25×C229
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C22×C229 ◁ G

898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3664

Conjugacy classes & character table

7786 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#1790×C229, #1792×C229, #1795×C229, …
maximal normal subgroup of#1790×C229, #1792×C229, #1795×C229, …
maximal quotient ofC2×#518×C229, C2×#520×C229, C4×H(5,𝔽2)×C229, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 264);