Finite Group Databasebeta

C2×#22587673 #31978619

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22587673

Splittings

SylowC71 ⋊ C2×#1664

Subgroups

subgroupG/H
centerC23#14556096
commutator, cosocleC42×C71C24
FrattiniC42C23×D71
FittingC2×#489×C71C2
socleC23×C71#120
prime radicalC22×D4×C71D4
hypercenterC2×#489D71
hypocenterC71C2×#1664
LCSG ▷ C42×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 150735);