Finite Group Databasebeta

C4×#16836604 #28417397

order14912
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16836604

Splittings

SylowC233 ⋊ C4×M16

Subgroups

subgroupG/H
centerC2×C4C2×#11745400
commutatorC2×C233C2×C42
FrattiniC22C22×#11745400
FittingC42×C233C4
socleC22×C233C22×C4
prime radicalC22×D233C2×C4
cosocleC2×Dic233C23
hypercenterC42#11745400
hypocenterC233C4×M16
LCSG ▷ C2×C233 ▷ C233
UCSC1 ◁ C2×C4 ◁ C42

142 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7456

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14912, 1511);