Finite Group Databasebeta

← Prev (#32912891) Next (#32912893) →

Dic3×C25×C61 #32912892

order18300
automorphism?
homologyAbelianization (H1) = C4×C25×C61 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C25×C61
unambiguous semidirect productC3⋊(C4×C25×C61)

Splittings

derived, SylowC3 ⋊ C4×C25×C61
HallC3×C25×C61 ⋊ C4
HallC3×C61 ⋊ C4×C25
HallC3×C25 ⋊ C4×C61

Subgroups

subgroupG/H
center, hypercenterC2×C25×C61D3
commutator, hypocenterC3C4×C25×C61
FrattiniC2×C5C5×D3×C61
FittingC2×C3×C25×C61C2
socle, prime radicalC2×C3×C5×C61C2×C5
cosocleC2×C3×C5C2×C5×C61
LCSG ▷ C3
UCSC1 ◁ C2×C25×C61

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18300

Conjugacy classes & character table

9150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 15);