Finite Group Databasebeta

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C2×2−1+4×Dic61 #30586623

order15616
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×2−1+4×Dic61

Splittings

SylowC61 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC23C24×D61
commutatorC2×C61C25×C4
FrattiniC22C25×D61
Fitting, prime radicalC22×2−1+4×C61C2
socleC23×C61C25
cosocleC22×C61C26
hypercenterC22×2−1+4D61
hypocenterC61C2×C4×2−1+4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1076178);