Finite Group Databasebeta

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C22×#13095501 #20261511

order6208
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#13095501

Splittings

SylowC97 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23C22⋊D97
commutatorC4×C97C24
FrattiniC4C23×D97
FittingC22×Q8×C97C2
socleC23×C97D4
hypercenterC22×Q8D97
hypocenterC97C22×Q16
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

258 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#27142074, #27142075, #27142077, …
maximal normal subgroup of#27142074, #27142075, #27142077, …
maximal quotient ofC22×#15690733, C22×#15690734, C22×#15690743, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 1325);