Finite Group Databasebeta

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C23×C22⋊#66524 #44499628

order30636
automorphism?
homologyAbelianization (H1) = C9×C23 · Schur multiplier (H2) = C2

Aliases

direct productC23×C22⋊#66524
unambiguous semidirect productC22⋊(C23×#66524)
unambiguous semidirect product(C22×C23)⋊#66524

Splittings

derived, HallC22×C37 ⋊ C9×C23
HallC22×C23×C37 ⋊ C9
HallC23×C37 ⋊ C22⋊C9
HallC22×C23 ⋊ #66524
SylowC37 ⋊ C23×C22⋊C9
SylowC22 ⋊ C23×#66524

Subgroups

subgroupG/H
center, hypercenterC3×C23C22⋊(C37⋊C3)
commutator, hypocenterC22×C37C9×C23
FrattiniC3C23×C22⋊(C37⋊C3)
Fitting, socle, prime radicalC22×C3×C23×C37C3
cosocleC22×C3×C37C3×C23
LCSG ▷ C22×C37
UCSC1 ◁ C3×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15318

Conjugacy classes & character table

3588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 31);