Finite Group Databasebeta

C4×#17988646 #33084129

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

Aliases

direct productC4×#17988646

Splittings

FittingC42×C8×C73 ⋊ C2
SylowC73 ⋊ C4×#433

Subgroups

subgroupG/H
centerC2×C42C22×D73
commutatorC22×C73C22×C42
FrattiniC22×C4C23×D73
FittingC42×C8×C73C2
socleC23×C73C23×C4
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenterC42×C8D73
hypocenterC73C4×#433
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C42 ◁ C42×C8

970 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, 167713);