Finite Group Databasebeta

C2×#22559644 #30838122

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22559644

Splittings

SylowC67 ⋊ C2×#1681

Subgroups

subgroupG/H
centerC23#14524015
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
Fitting, prime radicalC2×#459×C67C2
socleC23×C67#121
hypercenterC2×#459D67
hypocenterC67C2×#1681
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 151859);