Finite Group Databasebeta

C4×#17989580 #34020109

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#17989580

Splittings

FittingC2×C4×Q8×C73 ⋊ C4
SylowC73 ⋊ C4×#419

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#64408
commutatorC4×C73C22×C42
FrattiniC2×C4C23×#64408
FittingC2×C4×Q8×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC23×D73C2×D4
cosocleC2×C4×D73C24
hypercenterC2×C4×Q8#64408
hypocenterC73C4×#419
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

1586 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1103693);