Finite Group Databasebeta

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C2×2−1+4×Dic71 #32904062

order18176
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×Dic71

Splittings

SylowC71 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC23C24×D71
commutatorC2×C71C25×C4
FrattiniC22C25×D71
Fitting, prime radicalC22×2−1+4×C71C2
socleC23×C71C25
cosocleC22×C71C26
hypercenterC22×2−1+4D71
hypocenterC71C2×C4×2−1+4
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C22×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1076178);