Finite Group Databasebeta

← Prev (#14519013) Next (#14519015) →

C4×#92404 #14519014

order1944
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C35

Aliases

direct productC4×#92404

Splittings

FittingC4×H(5,𝔽3) ⋊ C2
derived, SylowH(5,𝔽3) ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC3×C4C3⋊(C3⋊(C3⋊D3))
commutator, hypocenterH(5,𝔽3)C2×C4
Frattini, socleC2×C3C2×C3⋊(C3⋊(C3⋊D3))
FittingC4×H(5,𝔽3)C2
prime radicalC2×#92404C2
cosocleC2×H(5,𝔽3)C22
LCSG ▷ H(5,𝔽3)
UCSC1 ◁ C3×C4

2344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 108

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3408);