Finite Group Databasebeta

C2×#22558086 #30745795

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22558086

Splittings

SylowC67 ⋊ C2×#1293

Subgroups

subgroupG/H
centerC23C67⋊#95
commutatorC2×C4×C67C2×C42
FrattiniC23×C4C22×D67
FittingC22×C22⋊C8×C67C2
socleC23×C67#95
prime radicalC25×C67Q8
cosocleC23×C4×C67C23
hypercenterC22×C22⋊C8D67
hypocenterC67C2×#1293
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

906 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2704 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 59532);