Finite Group Databasebeta

C2×#22597827 #32864308

order18176
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22597827

Splittings

SylowC71 ⋊ C2×#3039

Subgroups

subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×C4×#41×C71C2
socleC23×C71C22×D4
prime radicalC22×#41×C71C22
hypercenterC2×C4×#41D71
hypocenterC71C2×#3039
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

2790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2864 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1036424);