Finite Group Databasebeta

← Prev (#37557172) Next (#37557174) →

C4×C52⋊C3×C79 #37557173

order23700
automorphism?
homologyAbelianization (H1) = C3×C4×C79 · Schur multiplier (H2) = C5

Aliases

direct productC4×C52⋊C3×C79
unambiguous semidirect product(C4×C52)⋊(C3×C79)

Splittings

Fitting, HallC4×C52×C79 ⋊ C3
derived, SylowC52 ⋊ C3×C4×C79
HallC52×C79 ⋊ C3×C4
HallC4×C52 ⋊ C3×C79

Subgroups

subgroupG/H
center, hypercenterC4×C79C52⋊C3
commutator, hypocenterC52C3×C4×C79
FrattiniC2C2×C52⋊C3×C79
FittingC4×C52×C79C3
socleC2×C52×C79C2×C3
prime radicalC2×C52⋊C3×C79C2
cosocleC2×C52C2×C3×C79
LCSG ▷ C52
UCSC1 ◁ C4×C79

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4740

Conjugacy classes & character table

3476 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23700, 56);