Finite Group Databasebeta

C22×C4×#11924005 #33244158

order18688
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×C4×#11924005

Splittings

FittingC23×C42×C73 ⋊ C2
SylowC73 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC24×C4C2×D73
commutatorC2×C73C23×C42
FrattiniC23C24×D73
FittingC23×C42×C73C2
socleC25×C73C23
prime radicalC25×D73C22
cosocleC23×C73C25
hypercenterC23×C42D73
hypocenterC73C22×C4×C22⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C24×C4 ◁ C23×C42

9534 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, 327742);