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D4×#13083443 #26015072

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

Aliases

direct productD4×#13083443

Splittings

FittingD4×C353 ⋊ C4
SylowC353 ⋊ C4×D4

Subgroups

subgroupG/H
center, FrattiniC2C22×#13083443
commutator, socleC2×C353C22×C4
FittingD4×C353C4
prime radicalD4×D353C2
cosocleC2×D353C23
hypercenterD4#13083443
hypocenterC353C4×D4
LCSG ▷ C2×C353 ▷ C353
UCSC1 ◁ C2 ◁ D4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

460 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD8×#13083443, SD16×#13083443, #36378826, …
maximal normal subgroup ofD8×#13083443, SD16×#13083443, #36378826, …
maximal quotient ofC22⋊C4×#13083443, C4⋊C4×#13083443, #36378734, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11296, 226);