Finite Group Databasebeta

C4×#17988488 #33007173

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

direct productC4×#17988488

Splittings

FittingC2×C4×C4⋊C4×C73 ⋊ C2
SylowC73 ⋊ C4×#390

Subgroups

subgroupG/H
centerC23×C4C22×D73
commutatorC22×C73C22×C42
FrattiniC24C23×D73
FittingC2×C4×C4⋊C4×C73C2
socle, cosocleC24×C73C24
prime radicalC23×D292C22
hypercenterC2×C4×C4⋊C4D73
hypocenterC73C4×#390
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2992 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 90757);