Finite Group Databasebeta

C4×#11745254 #16821832

order3712
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#11745254

Splittings

FittingC4×C4⋊C4×C29 ⋊ C2
SylowC29 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D29
commutatorC2×C29C22×C42
FrattiniC23C23×D29
FittingC4×C4⋊C4×C29C2
socle, cosocleC23×C29C24
prime radicalC23×D29C23
hypercenterC4×C4⋊C4D29
hypocenterC29C4×#117
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1856

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 6850);