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C7×C31×Dic13⋊C3 #46799249

order33852
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productC7×C31×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C7×C31)

Splittings

derived, SylowC13 ⋊ C3×C4×C7×C31
HallC7×C31×Dic13 ⋊ C3
HallC7×C31×C13⋊C3 ⋊ C4
HallC7×C13×C31 ⋊ C3×C4
HallC31×Dic13 ⋊ C3×C7
HallC31×C13⋊C3 ⋊ C4×C7
HallC13×C31 ⋊ C3×C4×C7
HallC7×Dic13 ⋊ C3×C31
HallC7×C13⋊C3 ⋊ C4×C31
HallC7×C13 ⋊ C3×C4×C31
HallDic13 ⋊ C3×C7×C31
HallC13⋊C3 ⋊ C4×C7×C31

Subgroups

subgroupG/H
center, hypercenterC2×C7×C31D13⋊C3
commutator, hypocenterC13C3×C4×C7×C31
FrattiniC2C7×C31×D13⋊C3
Fitting, socleC2×C7×C13×C31C2×C3
prime radicalC2×C7×C31×C13⋊C3C2
cosocleC2×C13C2×C3×C7×C31
LCSG ▷ C13
UCSC1 ◁ C2×C7×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

3472 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 44);