Finite Group Databasebeta

C2×#22559178 #30828003

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22559178

Splittings

SylowC67 ⋊ C2×#1604

Subgroups

subgroupG/H
centerC23#14524012
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
Fitting, prime radicalC2×#537×C67C2
socleC23×C67#120
hypercenterC2×#537D67
hypocenterC67C2×#1604
LCSG ▷ C22×C4×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#537

1480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1498 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 141740);