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C13×C31×Dic21 #46799231

order33852
automorphism?
homologyAbelianization (H1) = C4×C13×C31 · Schur multiplier (H2) = C1

Aliases

direct productC13×C31×Dic21
unambiguous semidirect productC3⋊(C13×Dic7×C31)
unambiguous semidirect productC7⋊(Dic3×C13×C31)

Splittings

derived, HallC3×C7 ⋊ C4×C13×C31
HallC3×C7×C13×C31 ⋊ C4
HallC7×C13×C31 ⋊ Dic3
HallC3×C13×C31 ⋊ Dic7
HallC3×C7×C31 ⋊ C4×C13
HallC3×C7×C13 ⋊ C4×C31
HallC7×C31 ⋊ Dic3×C13
HallC3×C31 ⋊ C13×Dic7
HallC7×C13 ⋊ Dic3×C31
HallC3×C13 ⋊ Dic7×C31
SylowC7 ⋊ Dic3×C13×C31
SylowC3 ⋊ C13×Dic7×C31

Subgroups

subgroupG/H
center, hypercenterC2×C13×C31D21
commutator, hypocenterC3×C7C4×C13×C31
FrattiniC2C13×C31×D21
Fitting, socle, prime radicalC2×C3×C7×C13×C31C2
cosocleC2×C3×C7C2×C13×C31
LCSG ▷ C3×C7
UCSC1 ◁ C2×C13×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33852

Conjugacy classes & character table

9672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 26);