Finite Group Databasebeta

C2×#22558117 #30746192

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

Aliases

direct productC2×#22558117

Splittings

SylowC67 ⋊ C2×#1306

Subgroups

subgroupG/H
centerC23C67⋊#95
commutatorC23×C67C2×C42
FrattiniC23×C4C22×D67
FittingC2×#381×C67C2
socleC23×C67#95
prime radicalC25×C67C2×C4
cosocleC23×C4×C67C23
hypercenterC2×#381D67
hypocenterC67C2×#1306
LCSG ▷ C23×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#381

942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 59929);