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C4×C22⋊D367 #26044222

order11744
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D367

Splittings

FittingC22×C4×C367 ⋊ C2
SylowC367 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D367
commutatorC2×C367C22×C4
FrattiniC22C22×D367
FittingC22×C4×C367C2
socle, cosocleC22×C367C23
prime radicalC2×C22⋊D367C2
hypercenterC22×C4D367
hypocenterC367C4×D4
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2948 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D367)⋊C8, C8×C22⋊D367, #37554254, …
maximal normal subgroup of(C22⋊D367)⋊C8, C8×C22⋊D367, #37554254, …
maximal quotient ofC4×C22⋊Dic367, C4×(C2×D367)⋊C4, C4×Dic367⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11744, 107);