Finite Group Databasebeta

C2×#41×Dic142 #32904524

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC2×#41×Dic142

Splittings

SylowC71 ⋊ C2×Q8×#41

Subgroups

subgroupG/H
centerC22×C4C23×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×C4×#41×C71C2
socleC23×C71C25
prime radicalC22×#41×C71C22
hypercenterC2×C4×#41D71
hypocenterC71C2×Q8×#41
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

7522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1076640);