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C13×(C31⋊C3)⋊Dic7 #46799287

order33852
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C31⋊C3)⋊Dic7
unambiguous semidirect product(C31⋊C3)⋊(C13×Dic7)

Splittings

derived, HallC7×C31 ⋊ C3×C4×C13
HallC13×Dic217 ⋊ C3
HallC7×C13×C31⋊C3 ⋊ C4
HallC7×C13×C31 ⋊ C3×C4
HallC13×C31⋊C3 ⋊ Dic7
HallDic217 ⋊ C3×C13
HallC7×C31⋊C3 ⋊ C4×C13
HallC13×C31 ⋊ C3×Dic7
HallC31⋊C3 ⋊ C13×Dic7
HallC7×C13 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×C13×Dic7
SylowC7 ⋊ C13×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C13(C31⋊C3)⋊D7
commutator, hypocenterC7×C31C3×C4×C13
FrattiniC2C13×(C31⋊C3)⋊D7
Fitting, socleC2×C7×C13×C31C2×C3
prime radicalC2×C7×C13×C31⋊C3C2
cosocleC2×C7×C31C2×C3×C13
LCSG ▷ C7×C31
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 82);