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C4×2−1+4×D59 #29495294

order15104
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×2−1+4×D59

Splittings

FittingC4×2−1+4×C59 ⋊ C2
SylowC59 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC2×C4C24×D59
commutatorC2×C59C25×C4
FrattiniC22C25×D59
FittingC4×2−1+4×C59C2
socle, cosocleC22×C59C26
prime radicalC2×2−1+4×D59C2
hypercenterC4×2−1+4D59
hypocenterC59C2×C4×2−1+4
LCSG ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076173);