Finite Group Databasebeta

C2×#22561517 #30883757

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22561517

Splittings

SylowC67 ⋊ C2×#2054

Subgroups

subgroupG/H
centerC24D4×D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
Fitting, prime radicalC23×D8×C67C2
socleC24×C67C2×D4
hypercenterC23×D8D67
hypocenterC67C2×#2054
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

1918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 197494);