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C22×#14582115 #24925057

order10784
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC22×#14582115

Splittings

Fitting, socleC22×C337 ⋊ C8
derived, SylowC337 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22#14582115
commutator, hypocenterC337C22×C8
FrattiniC1G
Fitting, socleC22×C337C8
prime radicalC22×D337C4
cosocle#13062438C23
LCSG ▷ C337
UCSC1 ◁ C22

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#14582115)⋊C4, C2×C4×#14582115, C2×C22⋊#14582115, …
maximal normal subgroup of(C2×#14582115)⋊C4, C2×C4×#14582115, C2×C22⋊#14582115, …
maximal quotient ofC2×C4×#14582115, C2×C22⋊#14582115, C2×C4⋊#14582115, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10784, 244);