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C13⋊C3×Dic77 #26046451

order12012
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×Dic77
unambiguous semidirect productC11⋊(Dic7×C13⋊C3)

Splittings

derived, HallC7×C11×C13 ⋊ C3×C4
HallC13×Dic77 ⋊ C3
HallC7×C11×C13⋊C3 ⋊ C4
HallC11×C13⋊C3 ⋊ Dic7
HallC7×C13⋊C3 ⋊ Dic11
HallC11×C13 ⋊ C3×Dic7
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×Dic77
SylowC11 ⋊ Dic7×C13⋊C3
SylowC7 ⋊ C13⋊C3×Dic11

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C13⋊C3×D77
commutator, hypocenterC7×C11×C13C3×C4
Fitting, socle, cosocleC2×C7×C11×C13C2×C3
prime radicalC2×C7×C11×C13⋊C3C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC13⋊C3×C11⋊(ΓL(1,𝔽8)⋊C4), C3×C13⋊C3×Dic77, C13⋊C3×Dic231
maximal normal subgroup ofC13⋊C3×C11⋊(ΓL(1,𝔽8)⋊C4), C3×C13⋊C3×Dic77
maximal quotient ofC13⋊C9×Dic77, C3×C13⋊C3×Dic77, C13⋊C3×Dic231

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 41);