Finite Group Databasebeta

C2×#22558084 #30745775

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

Aliases

direct productC2×#22558084

Splittings

SylowC67 ⋊ C2×#1292

Subgroups

subgroupG/H
centerC23C67⋊#95
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC22×C4⋊C8×C67C2
socleC23×C67#95
prime radicalC24×C67C4⋊C4
cosocleC2×C42×C67C23
hypercenterC22×C4⋊C8D67
hypocenterC67C2×#1292
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4⋊C8

690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 59512);