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C22×#13095525 #20261867

order6208
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC22×#13095525

Splittings

Fitting, socleC22×C97 ⋊ C16
derived, SylowC97 ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC22#13095525
commutator, hypocenterC97C22×C16
FrattiniC1G
Fitting, socleC22×C97C16
LCSG ▷ C97
UCSC1 ◁ C22

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#13095525)⋊C4, C2×C4×#13095525, C2×C22⋊#13095525, …
maximal normal subgroup of(C2×#13095525)⋊C4, C2×C4×#13095525, C2×C22⋊#13095525, …
maximal quotient ofC2×C4×#13095525, C2×C22⋊#13095525, C2×C4⋊#13095525, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 1681);