Finite Group Databasebeta

← Prev (#26014952) Next (#26014954) →

C4×C22⋊D353 #26014953

order11296
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D353

Splittings

FittingC22×C4×C353 ⋊ C2
SylowC353 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D353
commutatorC2×C353C22×C4
FrattiniC22C22×D353
FittingC22×C4×C353C2
socle, cosocleC22×C353C23
prime radicalC2×C22⋊D353C2
hypercenterC22×C4D353
hypocenterC353C4×D4
LCSG ▷ C2×C353 ▷ C353
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2836 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#36377850, C8×C22⋊D353, #36377855, …
maximal normal subgroup of#36377850, C8×C22⋊D353, #36377855, …
maximal quotient ofC4×C22⋊Dic353, C4×#19150714, C4×#19150716, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11296, 107);