Finite Group Databasebeta

C23×C4⋊Dic3 #11764181

order1104
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C4×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×C4⋊Dic3
unambiguous semidirect productC4⋊(Dic3×C23)

Splittings

HallC3×C23 ⋊ C4⋊C4
SylowC3 ⋊ C4⋊C4×C23

Subgroups

subgroupG/H
centerC22×C23C2×D3
commutatorC2×C3C2×C4×C23
FrattiniC22C2×D3×C23
FittingC2×C3×C4×C23C2
socle, prime radicalC22×C3×C23C22
cosocleC22×C3C22×C23
hypercenterC2×C4×C23D3
hypocenterC3C4⋊C4×C23
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C23 ◁ C2×C4×C23

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1104

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1104, 56);