Finite Group Databasebeta

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C7×C11×Dic115 #47978378

order35420
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×Dic115

Splittings

derived, HallC5×C23 ⋊ C4×C7×C11
HallC5×C7×C11×C23 ⋊ C4
HallC7×C11×C23 ⋊ Dic5
HallC5×C11×C23 ⋊ C4×C7
HallC5×C7×C23 ⋊ C4×C11
HallC5×C7×C11 ⋊ Dic23
HallC11×C23 ⋊ C7×Dic5
HallC7×C23 ⋊ C11×Dic5
HallC5×C11 ⋊ C7×Dic23
HallC5×C7 ⋊ C11×Dic23
SylowC23 ⋊ C7×C11×Dic5
SylowC5 ⋊ C7×C11×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D115
commutator, hypocenterC5×C23C4×C7×C11
FrattiniC2C7×C11×D115
Fitting, socle, prime radicalC2×C5×C7×C11×C23C2
cosocleC2×C5×C23C2×C7×C11
LCSG ▷ C5×C23
UCSC1 ◁ C2×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35420

Conjugacy classes & character table

9086 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35420, 12);