Finite Group Databasebeta

C2×C4×#14524073 #31719903

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#14524073

Splittings

SylowC67 ⋊ C2×C4×#137

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×C4×#41×C67C2
socleC23×C67C22×D4
prime radicalC22×#41×C67C22
cosocleC2×C4×C67C25
hypercenterC2×C4×#41D67
hypocenterC67C2×C4×#137
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

2810 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033640);