Finite Group Databasebeta

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C22⋊C4×#10624382 #26042217

order11584
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC22⋊C4×#10624382

Splittings

FittingC22⋊C4×C181 ⋊ C4
SylowC181 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×#10624382
commutatorC2×C181C2×C42
FittingC22⋊C4×C181C4
socleC22×C181C22×C4
prime radicalC23×D181C22
cosocleC22×D181C23
hypercenterC22⋊C4#10624382
hypocenterC181C4×C22⋊C4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22⋊C4

258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

490 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#99×#10624382, C2×C22⋊C4×#10624382, #117×#10624382, …
maximal normal subgroup of#99×#10624382, C2×C22⋊C4×#10624382, #117×#10624382, …
maximal quotient of#95×#10624382, #37548894, #37548896, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11584, 1487);