Finite Group Databasebeta

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C52×C3⋊(Dic37⋊C3) #45686103

order33300
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×C3⋊(Dic37⋊C3)
unambiguous semidirect productC3⋊(C52×Dic37⋊C3)
unambiguous semidirect productDic111⋊(C3×C52)
unambiguous semidirect product(C5×Dic111)⋊(C3×C5)

Splittings

derivedC3×C37 ⋊ C3×C4×C52
HallC3×C52×C37⋊C3 ⋊ C4
HallC52×C37 ⋊ C3×Dic3
HallC3×C37⋊C3 ⋊ C4×C52
SylowC37 ⋊ C3×C52×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C52C3⋊(D37⋊C3)
commutator, hypocenterC3×C37C3×C4×C52
FrattiniC2C52×C3⋊(D37⋊C3)
Fitting, socleC2×C3×C52×C37C2×C3
prime radicalC2×C3×C52×C37⋊C3C2
cosocleC2×C3×C37C2×C3×C52
LCSG ▷ C3×C37
UCSC1 ◁ C2×C52

224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11100

Conjugacy classes & character table

1350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 376);