Finite Group Databasebeta

C4×#16812745 #28376239

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#16812745

Splittings

FittingC4×#41×C109 ⋊ C2
SylowC109 ⋊ C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C23×D109
commutatorC2×C109C24×C4
FrattiniC22C24×D109
FittingC4×#41×C109C2
socle, cosocleC22×C109C25
prime radicalC2×#16812745C2
hypercenterC4×#41D109
hypocenterC109C4×H(5,𝔽2)
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C4×#41

1660 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17717);