Finite Group Databasebeta

C2×#22558468 #30777520

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22558468

Splittings

SylowC67 ⋊ C2×#1442

Subgroups

subgroupG/H
centerC25C22×D67
commutatorC23×C67C23×C4
FrattiniC24C23×D67
FittingC23×C4⋊C4×C67C2
socle, prime radicalC25×C67C23
cosocleC24×C67C24
hypercenterC23×C4⋊C4D67
hypocenterC67C2×#1442
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C25 ◁ C23×C4⋊C4

2942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 91257);