Finite Group Databasebeta

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#534×C277 #31799668

order17728
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C277 · Schur multiplier (H2) = C25

Aliases

direct product#534×C277

Subgroups

subgroupG/H
center, socleC22×C277C24
commutator, Frattini, cosocleC22C24×C277
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C277 ◁ G

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4432

Conjugacy classes & character table

6094 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#47982085, #47982119, #47982153, …
maximal subgroup of#1595×C277, #1601×C277, #1607×C277, …
maximal normal subgroup of#1595×C277, #1601×C277, #1607×C277, …
maximal quotient of#2308×C277, #2315×C277, #2321×C277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17728, 215);