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C72×C11⋊AGL(1,𝔽5) #24924764

order10780
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C72×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C4
derived, HallC5×C11 ⋊ C4×C72
HallC72×C11 ⋊ AGL(1,𝔽5)
HallC5×C72 ⋊ Dic11
SylowC11 ⋊ C72×AGL(1,𝔽5)
SylowC5 ⋊ C72×Dic11

Subgroups

subgroupG/H
center, hypercenterC72C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C72
FrattiniC1G
Fitting, socleC5×C72×C11C4
prime radicalC72×D5×C11C2
cosocleD5×C11C2×C72
LCSG ▷ C5×C11
UCSC1 ◁ C72

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×ΓL(1,𝔽8)×C11⋊AGL(1,𝔽5), #3861×C11⋊AGL(1,𝔽5), #3862×C11⋊AGL(1,𝔽5), …
maximal normal subgroup ofC7×ΓL(1,𝔽8)×C11⋊AGL(1,𝔽5), #3861×C11⋊AGL(1,𝔽5), #3862×C11⋊AGL(1,𝔽5), …
maximal quotient ofC3×C72×C11⋊AGL(1,𝔽5), C72×C3⋊(C11⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 77);