Finite Group Databasebeta

C2×#22559454 #30831642

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

Aliases

direct productC2×#22559454

Splittings

SylowC67 ⋊ C2×#1648

Subgroups

subgroupG/H
centerC23#14524013
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC2×Q8⋊C8×C67C2
socle, prime radicalC23×C67#120
hypercenterC2×Q8⋊C8D67
hypocenterC67C2×#1648
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 145379);