Finite Group Databasebeta

C4×#17988652 #33084296

order18688
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#17988652

Splittings

FittingC4×C4⋊C8×C73 ⋊ C2
SylowC73 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC2×C42C22×D73
commutatorC2×C73C22×C4×C8
FrattiniC22×C4C23×D73
FittingC4×C4⋊C8×C73C2
socleC23×C73C23×C4
prime radicalC22×D292C2×C4
cosocleC22×C4×C73C24
hypercenterC4×C4⋊C8D73
hypocenterC73C4×C8×D4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 167880);