Finite Group Databasebeta

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C5×C7×Dic77 #24924733

order10780
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic77
unambiguous semidirect productC7⋊(C5×C7×Dic11)

Splittings

derivedC7×C11 ⋊ C4×C5×C7
HallC5×C72×C11 ⋊ C4
HallC72×C11 ⋊ C4×C5
HallC5×C72 ⋊ Dic11
HallC5×C11 ⋊ C7×Dic7
SylowC72 ⋊ C5×Dic11
SylowC11 ⋊ C5×C7×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D77
commutator, hypocenterC7×C11C4×C5×C7
FrattiniC2C5×C7×D77
Fitting, socle, prime radicalC2×C5×C72×C11C2
cosocleC2×C7×C11C2×C5×C7
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×C11⋊(ΓL(1,𝔽8)⋊C4), C5×C11⋊#10596873, C5×C11⋊#10596872, …
maximal normal subgroup ofC5×C7×C11⋊(ΓL(1,𝔽8)⋊C4), C5×C11⋊#10596873, C5×C11⋊#10596872, …
maximal quotient ofC5×C7×Dic231, C3×C5×C7×Dic77

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 46);