Finite Group Databasebeta

← Prev (#42124643) Next (#42124645) →

Dic3×C31×C52⋊C3 #42124644

order27900
automorphism?
homologyAbelianization (H1) = C3×C4×C31 · Schur multiplier (H2) = C5

Aliases

direct productDic3×C31×C52⋊C3
unambiguous semidirect productC3⋊(C4×C31×C52⋊C3)
unambiguous semidirect product(C52×Dic3)⋊(C3×C31)

Splittings

derivedC3×C52 ⋊ C3×C4×C31
HallC3×C31×C52⋊C3 ⋊ C4
HallC52×C31 ⋊ C3×Dic3
HallC3×C52⋊C3 ⋊ C4×C31
SylowC52 ⋊ C3×Dic3×C31

Subgroups

subgroupG/H
center, hypercenterC2×C31D3×C52⋊C3
commutator, hypocenterC3×C52C3×C4×C31
FrattiniC2D3×C31×C52⋊C3
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C31×C52⋊C3C2
cosocleC2×C3×C52C2×C3×C31
LCSG ▷ C3×C52
UCSC1 ◁ C2×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2046 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 391);