Finite Group Databasebeta

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C3×Dic3×C13×C61 #43269759

order28548
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C61 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C13×C61
unambiguous semidirect productC3⋊(C3×C4×C13×C61)

Splittings

derivedC3 ⋊ C3×C4×C13×C61
HallC32×C13×C61 ⋊ C4
HallC32×C61 ⋊ C4×C13
HallC32×C13 ⋊ C4×C61
SylowC32 ⋊ C4×C13×C61

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13×C61D3
commutator, hypocenterC3C3×C4×C13×C61
FrattiniC2C3×D3×C13×C61
Fitting, socle, prime radicalC2×C32×C13×C61C2
cosocleC2×C3C2×C3×C13×C61
LCSG ▷ C3
UCSC1 ◁ C2×C3×C13×C61

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9516

Conjugacy classes & character table

14274 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28548, 145);