Finite Group Databasebeta

C2×#22586448 #31912374

order18176
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22586448

Splittings

SylowC71 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC23#14556049
commutatorC8×C71C2×C42
FrattiniC22×C8C22×D71
FittingC22×#107×C71C2
socleC23×C71#102
prime radicalC24×C71SD16
cosocleC22×C8×C71C23
hypercenterC22×#107D71
hypocenterC71C2×#1387
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#107

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 84490);