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C22×#14272347 #21418633

order7456
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC22×#14272347

Splittings

Fitting, socleC22×C233 ⋊ C8
derived, SylowC233 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22#14272347
commutator, hypocenterC233C22×C8
FrattiniC1G
Fitting, socleC22×C233C8
LCSG ▷ C233
UCSC1 ◁ C22

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

148 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#14272347)⋊C4, C2×C4×#14272347, C2×C22⋊#14272347, …
maximal normal subgroup of(C2×#14272347)⋊C4, C2×C4×#14272347, C2×C22⋊#14272347, …
maximal quotient ofC2×C4×#14272347, C2×C22⋊#14272347, C2×C4⋊#14272347, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7456, 244);