Finite Group Databasebeta

C2×#22558338 #30770822

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

Aliases

direct productC2×#22558338

Splittings

SylowC67 ⋊ C2×#1395

Subgroups

subgroupG/H
centerC2×C4#14523958
commutatorC2×C4×C67C2×C42
FrattiniC2×#41C22×D67
FittingC2×#408×C67C2
socleC22×C67#342
prime radicalC22×#41×C67C22
cosocleC2×#41×C67C23
hypercenterC2×#408D67
hypocenterC67C2×#1395
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#408

766 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, 84559);