Finite Group Databasebeta

C4×#17989063 #33244233

order18688
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC4×#17989063

Splittings

FittingC42×Q8×C73 ⋊ C2
SylowC73 ⋊ C4×#519

Subgroups

subgroupG/H
centerC22×C4C23×D73
commutatorC2×C73C23×C42
FrattiniC23C24×D73
FittingC42×Q8×C73C2
socle, cosocleC23×C73C25
prime radicalC23×D73C24
hypercenterC42×Q8D73
hypocenterC73C4×#519
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C42×Q8

3402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

3016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 327817);