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C2×C43×#585 #19132410

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

Aliases

direct productC2×C43×#585

Subgroups

subgroupG/H
centerC2×C4×C43C24
commutator, Frattini, cosocleC2C26×C43
socleC22×C43C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ G

5956 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×#20606, C43×#20608, C43×#20610, …
maximal normal subgroup ofC43×#20606, C43×#20608, C43×#20610, …
maximal quotient ofC2×C43×#3428, C2×C4×H(5,𝔽2)×C43, C2×C4×2−1+4×C43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5504, 2325);