Finite Group Databasebeta

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C23×#10625337 #20258110

order6016
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×#10625337

Splittings

SylowC47 ⋊ C23×Q16

Subgroups

subgroupG/H
centerC24C22⋊D47
commutatorC4×C47C25
FrattiniC4C24×D47
FittingC23×Q8×C47C2
socleC24×C47D4
hypercenterC23×Q8D47
hypocenterC47C23×Q16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q8

1464 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

976 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#26123086, #26123087, #26123113, …
maximal normal subgroup of#26123086, #26123087, #26123113, …
maximal quotient ofC23×#13093947, C23×#13093948, C23×#13093957, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6016, 19232);