Finite Group Databasebeta

C2×C4×#14556551 #33244173

order18688
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×#14556551

Splittings

FittingC2×C4×C22⋊C4×C73 ⋊ C2
SylowC73 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC23×C4C22×D73
commutatorC2×C73C23×C42
FrattiniC23C24×D73
FittingC2×C4×C22⋊C4×C73C2
socleC24×C73C24
prime radicalC23×C22⋊D73C22
cosocleC23×C73C25
hypercenterC2×C4×C22⋊C4D73
hypocenterC73C2×C42×D4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

5694 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, 327757);