Finite Group Databasebeta

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C3×C11×Dic77 #23779003

order10164
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×Dic77
unambiguous semidirect productC11⋊(C3×C11×Dic7)

Splittings

derivedC7×C11 ⋊ C3×C4×C11
HallC3×C7×C112 ⋊ C4
HallC7×C112 ⋊ C3×C4
HallC3×C112 ⋊ Dic7
SylowC112 ⋊ C3×Dic7
HallC3×C7 ⋊ C11×Dic11
SylowC7 ⋊ C3×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D77
commutator, hypocenterC7×C11C3×C4×C11
FrattiniC2C3×C11×D77
Fitting, socle, prime radicalC2×C3×C7×C112C2
cosocleC2×C7×C11C2×C3×C11
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C11⋊(Dic7⋊C9), C9×C11×Dic77, C3×C11×C11⋊(ΓL(1,𝔽8)⋊C4), …
maximal normal subgroup ofC11×C11⋊(Dic7⋊C9), C9×C11×Dic77, C3×C11×C11⋊(ΓL(1,𝔽8)⋊C4), …
maximal quotient ofC9×C11×Dic77, C3×C11×Dic231, C32×C11×Dic77

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 55);