Finite Group Databasebeta

C23×C22⋊#10596831 #33949411

order18688
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊#10596831

Splittings

SylowC73 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D73
commutatorC2×C73C24×C8
FrattiniC2×C4C24×D73
FittingC25×C4×C73C2
socleC25×C73C2×C4
prime radicalC26×C73C4
cosocleC2×C4×C73C25
hypercenterC25×C4D73
hypocenterC73C23×C22⋊C8
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

4768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1032995);