Finite Group Databasebeta

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C52×C7×Dic17 #26045388

order11900
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C4×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52×C7×Dic17

Splittings

derived, SylowC17 ⋊ C4×C52×C7
HallC52×C7×C17 ⋊ C4
HallC52×C17 ⋊ C4×C7
HallC7×C17 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52×C7D17
commutator, hypocenterC17C4×C52×C7
FrattiniC2C52×C7×D17
Fitting, socle, prime radicalC2×C52×C7×C17C2
cosocleC2×C17C2×C52×C7
LCSG ▷ C17
UCSC1 ◁ C2×C52×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC52×ΓL(1,𝔽8)×Dic17, C7×Dic17×C52⋊C3, Dic17×C7⋊(C52⋊C3), …
maximal normal subgroup ofC52×ΓL(1,𝔽8)×Dic17, C7×Dic17×C52⋊C3, Dic17×C7⋊(C52⋊C3), …
maximal quotient ofC52×C7×Dic51, C3×C52×C7×Dic17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 37);