Finite Group Databasebeta

C42×#11924017 #33084457

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC42×#11924017

Splittings

FittingC42×C8×C73 ⋊ C2
SylowC73 ⋊ C42×SD16

Subgroups

subgroupG/H
centerC2×C42D292
commutatorC4×C73C22×C42
FrattiniC22×C4C23×D73
FittingC42×C8×C73C2
socleC23×C73C22×D4
prime radicalC22×D292C23
cosocleC22×C4×C73C24
hypercenterC42×C8D73
hypocenterC73C42×SD16
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×C8

1230 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

4720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 168041);