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C22×H(5,𝔽2)×C43 #19132408

order5504
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C26×C43 · Schur multiplier (H2) = C214

Aliases

direct productC22×H(5,𝔽2)×C43

Subgroups

subgroupG/H
center, socleC23×C43C24
commutator, Frattini, cosocleC2C26×C43
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ G

6560 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2924 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC43×#20585, C43×#20586, C43×#20592, …
maximal normal subgroup ofC43×#20585, C43×#20586, C43×#20592, …
maximal quotient ofC22×C43×#518, C22×C43×#520, C2×C4×H(5,𝔽2)×C43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5504, 2323);