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C4×C22⋊D311 #23755669

order9952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D311

Splittings

FittingC22×C4×C311 ⋊ C2
SylowC311 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D311
commutatorC2×C311C22×C4
FrattiniC22C22×D311
FittingC22×C4×C311C2
socle, cosocleC22×C311C23
prime radicalC2×C22⋊D311C2
hypercenterC22×C4D311
hypocenterC311C4×D4
LCSG ▷ C2×C311 ▷ C311
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D311)⋊C8, C8×C22⋊D311, #34091762, …
maximal normal subgroup of(C22⋊D311)⋊C8, C8×C22⋊D311, #34091762, …
maximal quotient ofC4×C22⋊Dic311, C4×(C2×D311)⋊C4, C4×Dic311⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9952, 107);