Finite Group Databasebeta

← Prev (#37557160) Next (#37557162) →

C5×Dic5×C79⋊C3 #37557161

order23700
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic5×C79⋊C3
unambiguous semidirect product(Dic5×C79)⋊(C3×C5)
unambiguous semidirect product(C5×Dic5×C79)⋊C3

Splittings

derivedC5×C79 ⋊ C3×C4×C5
HallC5×Dic5×C79 ⋊ C3
HallC52×C79⋊C3 ⋊ C4
HallC52×C79 ⋊ C3×C4
SylowC79 ⋊ C3×C5×Dic5
SylowC52 ⋊ C4×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D5×C79⋊C3
commutator, hypocenterC5×C79C3×C4×C5
FrattiniC2C5×D5×C79⋊C3
Fitting, socleC2×C52×C79C2×C3
prime radicalC2×C52×C79⋊C3C2
cosocleC2×C5×C79C2×C3×C5
LCSG ▷ C5×C79
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1580

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23700, 44);