Finite Group Databasebeta

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C5×C7×Dic221 #44525854

order30940
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic221

Splittings

derived, HallC13×C17 ⋊ C4×C5×C7
HallC5×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ C4×C5
HallC5×C13×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ Dic13
HallC5×C7×C13 ⋊ Dic17
HallC7×C17 ⋊ C5×Dic13
HallC7×C13 ⋊ C5×Dic17
HallC5×C17 ⋊ C7×Dic13
HallC5×C13 ⋊ C7×Dic17
SylowC17 ⋊ C5×C7×Dic13
SylowC13 ⋊ C5×C7×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D221
commutator, hypocenterC13×C17C4×C5×C7
FrattiniC2C5×C7×D221
Fitting, socle, prime radicalC2×C5×C7×C13×C17C2
cosocleC2×C13×C17C2×C5×C7
LCSG ▷ C13×C17
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30940

Conjugacy classes & character table

7840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 4);